Question

the inequality $2.75x + 1.95 \leq 12$ models the situation, where
what is the maximum number of hamburgers derrick can buy?

a. 2 hamburgers

b. 3 hamburgers

c. 4 hamburgers

d. 5 hamburgers

Explanation:

Step1: Subtract 1.95 from both sides

We start with the inequality \(2.75x + 1.95 \leq 12\). Subtract 1.95 from both sides:
\(2.75x + 1.95 - 1.95 \leq 12 - 1.95\)
Simplifying gives \(2.75x \leq 10.05\).

Step2: Divide by 2.75

Now divide both sides by 2.75 to solve for \(x\):
\(x \leq \frac{10.05}{2.75}\)
Calculating \(\frac{10.05}{2.75} \approx 3.65\).

Since \(x\) represents the number of hamburgers (a non - negative integer), the maximum integer value of \(x\) that satisfies the inequality is 3.

Answer:

B. 3 hamburgers